how to Voronoi-fracture with Chebychev, Manhattan, or Minkowski?
It is not possible natively. And there isn't an easy way ...
You can try create black&amp;white image. I wanted suggest to use newly implemented Trace to GreasePencil, but it didn't work without issues for this kind of image.

So probably would be better to use other app to vectorise (trace) image as Line Art and import as SVG back to Blender, Convert to Mesh, Delete by Limited Dissolve - angle 35°in this case (or dicrease curve resolution to 1 before convert to mesh), Merge by Distance.

Add Plane, select both objects, switch to edit mode and use Knife Project to split plane into parts.



There was a script FractureMe2d with this feature - split plane by image. It was a part of FractureMe file from pildanovak for Blender2.49 that worked at glance. Abandoned.